Biomarkers play an important role in medical research, and their use is being advocated in the detection, diagnosis, staging, treatment and management of a variety of diseases, including cancer. Using novel genomic and proteomic technologies, new biomarkers are constantly being discovered. Biomarkers are viewed by some as the most critical component in moving forward translational research in cancer. They are central to the critical path, articulated by the FDA, for enhancing drug development. There are several areas where statistical consideration would enhance the utility of biomarkers. First, many researchers have suggested that a single biomarker will be insufficient for prediction and that a panel of biomarkers will be necessary. This leads to the question of how to combine the biomarkers in an "optimal" manner. Second, many of the candidate biomarkers might be used as surrogate endpoints in randomized trials. Finally, for many biomarkers assumptions of monotonicity are a-priori known, e.g. increasing levels of biomarker are associated with increased disease risk. It would be valuable to have available statistical procedures that make use of this knowledge to improve the utility of the biomarkers. In this grant, we will be developing several new statistical modeling procedures for biomarker data in cancer studies. They are summarized in the following aims: Specific Aim 1: Development of semiparametric and nonparametric multivariate isotonic regression modelling procedures for biomarkers. (a) Two-stage estimation procedures for bivariate isotonic regression models and attendant nonparametric and semiparametric profile likelihood ratio inference procedures. (b) Isotonic estimation methods with ordered categorical covariates for censored data. Specific Aim 2: Development of statistical methods for the analysis of surrogate endpoints in a single-trial and multiple-trial framework. (a) Counterfactual-based modelling approach to the analysis of surrogate endpoints. (b) Shrinkage estimation approaches to the analysis of surrogate endpoints. (c) Semi-competing risks methodology for the analysis of surrogate endpoints. Specific Aim 3: Development of hybrid model averaging methods and attendant projection-based framework for combining biomarkers to optimize predictive accuracy. PUBLIC HEALTH RELEVANCE: Statistical Methods for Cancer Biomarkers. Biomarkers are measurements that can be taken from patient, for example from a simple blood test. Biomarkers do not measure how the patients feel or symptoms they have, never-the-less they may be very useful to give early detection of a disease, or to monitor how the treatment is working, or to assess whether a new treatment if effective. The aim of this grant is to develop valid methods of analyzing datasets of biomarkers, that get the most information out of the data.